Determination of Cache's Capacity and its Matching Storage Hierarchy

The optimum capacity of a cache memory with given access time is determined analytically based upon a model of linear storage hierarchies wherein both the hit ratio function and the device technology-cost function are assumed to be power functions. Explicit formulas for the capacities and access times of the storage levels in the matching hierarchy of required capacity and allowable cost are derived. The optimal number of storage levels in a hierarchy is shown to increase linearly with the logarithm of the ratio of the required hierarchy capacity and the cache capacity.